How do I prevent Blender adding an index-suffix to the objects' names?
When you delete an object, not all information about it will be deleted. Its mesh data will remain in the file. So if you want to delete the mesh data, open Outliner in Orphan data mode and click on Purge All - it will delete all mesh data that are not used in the scene, and free names.



Normally, object and mesh data can use different names, but the obj-import script makes these names the same. That's the reason why a new object gets the  old name, but obj-import gets a new one.